{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:05:35Z","timestamp":1760238335459,"version":"build-2065373602"},"reference-count":17,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2020,8,6]],"date-time":"2020-08-06T00:00:00Z","timestamp":1596672000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IJGI"],"abstract":"<jats:p>Sometimes it is necessary to know the transformation to apply to a mapping shape in order to locate its true place. Such an operation can be computed if a corresponding reference object exists and we can identify corresponding points in both shapes. Nevertheless our approach does not need to match any corresponding point beforehand. The method proposed defines a polygon in the frequency domain\u2014two periodic functions are derived from a polygonal or polygon. According to the theory of elliptic Fourier descriptors those two periodic functions can be expressed by Fourier expansions. The transformation can be computed using the coefficients of the harmonics from the corresponding shapes without taking into account where each polygon vertex is placed in the spatial domain. The transformation parameters will be derived by a least squares approach. The geomatics and geosciences applications of this method go from photogrammetry, geographic information system, computer vision, to cadaster and real estates.<\/jats:p>","DOI":"10.3390\/ijgi9080482","type":"journal-article","created":{"date-parts":[[2020,8,6]],"date-time":"2020-08-06T09:41:21Z","timestamp":1596706881000},"page":"482","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Fourier-Based Automatic Transformation between Mapping Shapes\u2014Cadastral and Land Registry Applications"],"prefix":"10.3390","volume":"9","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3808-1857","authenticated-orcid":false,"given":"Juan Francisco","family":"Reinoso-Gordo","sequence":"first","affiliation":[{"name":"Departamento de Expresi\u00f3n Gr\u00e1fica Arquitect\u00f3nica y en la Ingenier\u00eda, Universidad de Granada, 18071 Granada, Spain"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4500-9781","authenticated-orcid":false,"given":"Roc\u00edo","family":"Romero-Zaliz","sequence":"additional","affiliation":[{"name":"Departamento de Ciencias de la Computaci\u00f3n e Inteligencia Artificial, Universidad de Granada, 18071 Granada, Spain"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9167-9818","authenticated-orcid":false,"given":"Carlos","family":"Le\u00f3n-Robles","sequence":"additional","affiliation":[{"name":"Departamento de Expresi\u00f3n Gr\u00e1fica Arquitect\u00f3nica y en la Ingenier\u00eda, Universidad de Granada, 18071 Granada, Spain"}]},{"given":"Jes\u00fas","family":"Mataix-SanJuan","sequence":"additional","affiliation":[{"name":"Departamento de Expresi\u00f3n Gr\u00e1fica Arquitect\u00f3nica y en la Ingenier\u00eda, Universidad de Granada, 18071 Granada, Spain"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2124-5018","authenticated-orcid":false,"given":"Marcelo","family":"Antonio Nero","sequence":"additional","affiliation":[{"name":"Departamento de Cartografia, Universidade Federal de Minas Gerais, 31270 Belo Horizonte, Brazil"}]}],"member":"1968","published-online":{"date-parts":[[2020,8,6]]},"reference":[{"key":"ref_1","unstructured":"Zhang, D., and Lu, G. (2002, January 22\u201325). A Comparative Study of Fourier Descriptors for Shape Representation and Retrieval. Proceedings of the Fifth Asian Conference Computer Vision (ACCV 2002), Melbourne, Australia."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"142","DOI":"10.1109\/TPAMI.2005.21","article-title":"WARP: Accurate Retrieval of Shapes Using Phase of Fourier Descriptors and Time Warping Distance","volume":"27","author":"Bartolini","year":"2005","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"100","DOI":"10.1109\/TPAMI.2003.1159948","article-title":"Representation and self-similarity of shapes","volume":"25","author":"Geiger","year":"2003","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1109\/34.368168","article-title":"An Experimental Comparison of Autoregressive and Fourier-Based Descriptors in 2D Shape Classification","volume":"17","author":"Kauppinen","year":"1997","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_5","first-page":"1771","article-title":"Experiments with Edge-Based Stereo Matching","volume":"55","author":"Greenfel","year":"1989","journal-title":"Photogramm. Eng. Remote. Sens."},{"key":"ref_6","unstructured":"Yi-Hsing, T., and Shenk, T. (1992, January 2\u201314). A least-squares approach to matching lines with Fourier descriptors. Proceedings of the ISPRS (Commission III), Washington, DC, USA."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1023\/B:VISI.0000029664.99615.94","article-title":"Distinctive image features from scale-invariant keypoints","volume":"60","author":"Lowe","year":"2004","journal-title":"Int. J. Comput. Vis."},{"key":"ref_8","unstructured":"Hartley, R., and Zisserman, A. (2000). Multiple View Geometry in Computer Vision, Cambridge University Press. [1st ed.]."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1016\/j.optlaseng.2018.02.003","article-title":"A method of solving tilt illumination for multiple distance phase retrieval","volume":"106","author":"Guo","year":"2018","journal-title":"Opt. Lasers Eng."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"15122","DOI":"10.1364\/OE.391713","article-title":"High-resolution imaging system with an annular aperture of coded phase masks for endoscopic applications","volume":"28","author":"Dubey","year":"2020","journal-title":"Opt. Express"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"130","DOI":"10.1016\/j.jhydrol.2010.01.017","article-title":"A priori horizontal displacement (HD) estimation of hydrological features when versioned DEMs are used","volume":"384","author":"Reinoso","year":"2010","journal-title":"J. Hydrol."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"272","DOI":"10.1016\/j.isprsjprs.2010.10.008","article-title":"An algorithm for automatically computing horizontal shift between homologous contours from DTMs","volume":"66","author":"Reinoso","year":"2011","journal-title":"Isprs J. Photogramm. Remote. Sens."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"3556","DOI":"10.1016\/j.matcom.2009.04.006","article-title":"The Frenet frame beyond classical differential geometry: Application to cartographic generalization of roads","volume":"79","author":"Reinoso","year":"2009","journal-title":"Math. Comput. Simul."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"269","DOI":"10.1109\/TC.1972.5008949","article-title":"Fourier descriptors for plane closed curves","volume":"100","author":"Zahn","year":"1972","journal-title":"IEEE Trans. Comput."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.patcog.2003.07.008","article-title":"Review of shape representation and description techniques","volume":"37","author":"Zhang","year":"2004","journal-title":"Pattern Recognit."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"236","DOI":"10.1016\/0146-664X(82)90034-X","article-title":"Eliptic Fourier Features of a closed Contour","volume":"18","author":"Kuhl","year":"1982","journal-title":"Comput. Graph. Image Process."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"535","DOI":"10.1016\/0031-3203(87)90080-X","article-title":"New Forms of Shape Invariants from Elliptic Fourier Descriptors","volume":"20","author":"Lin","year":"1987","journal-title":"Pattern Recognit."}],"container-title":["ISPRS International Journal of Geo-Information"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2220-9964\/9\/8\/482\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T09:56:57Z","timestamp":1760176617000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2220-9964\/9\/8\/482"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,8,6]]},"references-count":17,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2020,8]]}},"alternative-id":["ijgi9080482"],"URL":"https:\/\/doi.org\/10.3390\/ijgi9080482","relation":{},"ISSN":["2220-9964"],"issn-type":[{"type":"electronic","value":"2220-9964"}],"subject":[],"published":{"date-parts":[[2020,8,6]]}}}